P4P5P6: Set Method (1 free with every multiple of)

Set method of many variations are taught since P3.

Such questions require students to count in multiples of certain number and use those multiples to calculate the value of such sets.

For the type of questions shown below, students will also need to understand what are "Complete Sets" and "Incomplete Sets".

Such questions are common in Section B and C of P4 exams and also in Paper 1 of P5 and P6 exams.

Calculator usage is not allowed.

At a fruit stall, apples are sold at $2 each.

For every 4 apples sold, an apple is given free.

a) What is the minimum amount needed to buy 21 apples?

b) What is the most number of apples that can be bought with $84?

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P4P5 Math: 2 Different Totals with 2 Different Quantities of 2 Different Items

Such questions presents 2 different type of items, each of different values.

The total of 2 different quantities of 2 items are given.

Without any comparison given, students must be able to make use of the 2 totals given in order to solve.

Such questions are common in Section C and Paper 1 of P4 and P5 exams.

Calculator usage is not allowed.

Similar questions of varying difficulties can also be found here and here.

3 pots and 5 lids costs $25.

4 pots and 3 lids costs $26.

How much does 6 lids cost?

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P6 Math: Catching up (Savings vs Spent vs Allowances)

Advance P6 questions such as these requires students to compare between daily differences and accumulated differences.

Such questions are common in P6 Prelim Paper 2.

Calculator usage is allowed.

An easier version of the question can be found here. (use for building concepts)

Esther's daily allowance is $0.40 more than Valerie's daily allowance.

Each girl spends the same amount of $1.50 every day and saves their remaining allowance.

When Esther saved $40, Valerie only managed to save $20.

How much was Valerie's daily allowance?

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P6 Math: Combination of Sets and Individual Units

This question type shows a total value resulting from a combination of multiple sets and mutiple single units without sets. 

These questions are common in Paper 2 of P6 exam papers.

Calculator usage is allowed.

Ivan is a fishmonger at the local market.

Each customer that buys 3 fish will get one free.

Each fish is sold at $12.

Last week, his customers either bought 1 or 3 fish.

Ivan collected $888 from the sale of his fish last week and gave away 21 free fish.

How many of his customers bought only 1 fish?

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P6 Math: Distance Speed and Time (Travelling Further than or Nearer than Mid-Point)

Another variation of the Distance Speed and Time.

2 persons are travelling from different start points and are moving towards the same destination along a straight line. One of them needs to travel past the mid-point but the other does not need to. (hence a shorter distance travelled).

Students need to know how to calculate the difference between the distance travelled between the 2 persons before solving the rest of the question.

Such questions are common in Paper 2 of P6 Prelim papers.

Calculator usage is allowed.

Ali and Bala are cycling from each of their separate houses towards Carl's house.

Bala's house is nearer to Carl's house than Ali's.

Both boys started their journey at the same time.

There is a supermarket in the mid-point between Ali's and Bala's house.

This supermarket is 560m away from Carl's house.

Ali cycled at a speed 140m/min faster than Bala.

Ali arrived at Carl's house at the same time as Bala.

a) How much further did Ali cycle than Bala to reach Carl's house?

b) If both boys started their journey at 4.50 p.m., at what time did they reach Carl's house?

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P5 Math: Ratio Basics (3 parties)

Ratio of 3 parties merely expresses the simplest form between 3 values and are not representing the exact value.

With one or more values given, students must make be able to derive the other values by means of multiplication or division.

Such questions usually appear in P5 Paper 1.

Calculator usage is not allowed.

Tricia, Belinda and Alicia has baked some muffins in the ratio of 4:3:1 respectively.

They baked a total of 640 muffins.

How many more muffins than Alicia did Tricia bake?

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P5/P6 Math: 3 Item Types with Different Quantities and Values

Such questions uses fraction and multiples(ratio) to give a breakdown of the distribution of 3 different items. Each of the item have different values and the total value of all quantities of 3 items is also provided.

Such questions are common in Paper 2 of P5 exams.

Calculator usage is allowed.

Erica bought a number of durians,watermelons and jackfruits 

from the market and spent $620 altogether.

¹/₂ of all the fruits bought were durians.

The ratio of the number of watermelons to jackfruits bought was 3:2.

Each durian costs $20, each watermelon $4 and each jackfruit was $6.

How many durians did Erica buy?

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P3/P4 Math: Fitting Equal Quantities into Containers with Remainder

The following question requires basic division so as to find out how many containers can be fitted with equal quantities but there will be some remainder after performing the division.

Such questions are common in P4 exams in Section A or B.

Mrs Lim is planning an excursion for her 60 students.

She needs to ferry the students and herself to the Science Center.

A mini-bus can sit up to 12 people.

What is the least number of mini-buses needed 

to ferry the students and herself to the Science Center?

Typical 12-seater mini-bus

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P6 Math: Fractions with Different Values

Such "fraction" questions are further complicated by having different values tagged to each group. Each of the "fraction of total" and "fraction of remaining" and "left" groups have different values/scores/points.

These questions often appear in Paper 2.

Calculator usage is allowed.

During a carnival, a total of 1748 play tokens were given out free to children whom visited.

¹/₄ of the children received 5 tokens each and 

²/₅ of the remaining children received 4 tokens each.

The rest of the children each received 3 tokens.

How many children visited the carnival?

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P5 Math: Set Method (Total Given)

Set method, often confused with assumption, because the total value is given.

Students need to differentiate between the 2 by noticing that the total quantities of both items were not given, hence not able to "assume".

Such "Set" questions often appear in Paper 2 of P5 exam papers.

Calculator usage is allowed.

More of such P5 set questions here.

Greg bought 5 times as many toy cars as toy trucks.

Each toy car costs $2 and each toy truck costs $5.

He spent a total of $120 of all the toy cars and toy trucks.

How many toy cars did Greg buy?

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